The idea of voting on the quality of posts is obviously ingenious. However, why did Jeff and Joel decide for the up/down-vote scheme? Wouldn't a scoring system1 be more helpful?

My thought is, if few people but specialists find a low-view question awesome, it will still end up with as little total (up-minus-down)-votes as a controversial high-view question, while something like List of freely available programming books with a broader audience get's up to 100x as many upvotes.

Yes, obviously more upvotes indicate more popularity, but the one thing that the system does maybe lack is a neutral vote. You can't say if someone who looked at a question but didn't vote just didn't feel like it or whether it's really a statement of "this question is kind of okay but not great".

What would be the disadvantages of taking instead a score scheme ranging from, say -2 ("This question may be on-topic, but it still totally sucks") to +2 ("I never knew I'd want to know this, but now I most certainly do"), and instead of upvotes showing the average score2? I mean, obviously the up/down-vote system works great, but I'm still curious about this.

1) like e.g. http://www.newgrounds.com/ uses, but let's add SE's once-only-vote-locking and maybe leave the high-rep-weighting away2) and maybe still a total score more or less equivalent to upvotes, but the average would tell more about neutral votes

Neutral vote == viewing and not voting. So score/views is a decent indicator of quality apart from insanely popular, off-topic, should-be-deleted questions.

I'm against a rating system replacing votes because it gives you no sense of proportion. A quesion with a rating of +1 could have been rated by one person or by a thousand. And then you have to look at views anyways and (depending on what you're interested in) maybe do some mental math, which is more or less no different than the votes/views math you might do.

well, I wouldn't suggest replacing the established system, I'm just curious about the reasoning. But viewing without voting is not exactly a neutral vote, since you could come back later from another IP only to then login and vote - I'm not sure what counts as a new view and what not, but it most likely includes unregistered users which could be the same person over and over again or even someone playing the system
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Tobias KienzlerOct 17 '11 at 20:10

On the right hand side is an indicator labelled "viewed". Take the split vote (you need rep for this) and noVotes = viewed - upVotes - downVotes. You can compute this manually when you feel so inclined or write a script to do it for you.

For example, on this question right now: noVotes = 42 - 2 - 4 = 36.

The number of views is a good indicator of the popularity. This is different from score which is the consensus opinion. I think both are interesting. Since both are there already, make of the information what you will.

I agree, the split is a good indicator, although you can only get this information if you have at least 1000rep on the site you want to see this. But as I commented on Matthew's answer, you cannot see neutral votes from that despite the views count. PS: Since the reason for the split-rep-requirement is claimed to be database access limitation, I think the SE wouldn't be too pleased by a script that asks for that very information on every post viewed, but I like the idea
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Tobias KienzlerOct 18 '11 at 6:16